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By combining the elastic-viscoelastic correspondence principle with the analytical solutions of anisotropic elasticity, the problems of two-dimensional linear anisotropic viscoelastic solids can be solved directly in the Laplace domain. After getting the solutions in the Laplace domain, their associated solutions in real time domain are determined by numerical inversion of Laplace transform. By using the codes developed by our research group for anisotropic elastic solids and adding some necessary functions, the anisotropic viscoelastic solids problems can be solved. Following this general adopted process, in this thesis the problems of holes, cracks, or inclusions in two-dimensional linear anisotropic viscoelastic solids are solved. Here, the hole can be elliptical or polygon-like; the crack can be a single crack, or two collinear cracks, or an interface crack; and the inclusion can be rigid, elastic or viscoelastic. The loads considered include the uniform load at infinity, and the point force applied at the arbitrary location. The solution of the point force is then employed as the fundamental solution of boundary element method which is used for further comparison of the analytical solutions. The accuracy and efficiency of the presented solutions are illustrated through four representative numerical examples which involve four isotropic viscoelastic and two anisotropic viscoelastic materials.

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